Question

A near U.V. photon of 300 nm is absorbe by a gas is red then remitted as two photons. One photon is red with wavelength 760 nm. Hence wavelength of the second photon is

Answer 1

It may be noted that energy of photon which is emitted as sun of the energy of two photons.
Energy absorbed, hv=`hc//lambda`
According to available information , `(hc)/(lambda)=(hc)/(lambda_(1))+(hc)/(lambda_(2)) , (1)/(lambda)=(1)/(lambda_(1))+(1)/(lambda_(2)) , (1)/(lambda_(2))=[(1)/(lambda)-(1)/(lambda_(2))]`
Now `lambda=300nm , lambda_(1)=760 nm , lambda_(2)` can be calculated as :
`(1)/(lambda_(2))=[(1)/(300)-(1)/(760)]=(760-300)/(300xx760) (nm^(-1))`
`(1)/(lambda_(2))=(460)/(760xx300)(nm^(-1))` or `lambda_(2)=(760xx300)/(460)(nm)=496 nm`.